Estimation of connectivity measures in gappy time series

• The problem of gaps in time series is solved without any assumption of the underlying dynamics.
• The accuracy of connectivity estimates is the same as for non-gappy time series of reduced length.
• The method compares favorably to a number of standard gap-filling techniques and the gap closure.
• The method can be applied to any time domain method of analysis of multivariate time series.
• The accuracy of the method is confirmed in a financial application.

A new method is proposed to compute connectivity measures on multivariate time series with gaps. Rather than removing or filling the gaps, the rows of the joint data matrix containing empty entries are removed and the calculations are done on the remainder matrix. The method, called measure adapted gap removal (MAGR), can be applied to any connectivity measure that uses a joint data matrix, such as cross correlation, cross mutual information and transfer entropy. MAGR is favorably compared using these three measures to a number of known gap-filling techniques, as well as the gap closure. The superiority of MAGR is illustrated on time series from synthetic systems and financial time series.